Elliptic curve data - 4200.e4

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  intrinsic_torsion	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '4200e', 'Clabel': '4200e4', 'Cnumber': 4, 'abc_quality': 0.958655911890363, 'absD': 297606960000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, -1, 0, 12592, 622812], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4200, 'degree': 18432, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4630024410488870912129155080', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [13799183324, 18600435], 'lmfdb_iso': '4200.e', 'lmfdb_label': '4200.e4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 504, 5184], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '70.6.0.a.1', '120.24.0.?', '140.24.0.?', '168.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 175], [3, 4, 1400], [5, 18, 168], [7, 8, 600]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.080660834365215812731509073506', 'prec': 107}, 'szpiro_ratio': 4.820969796297039, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -4, 0, 6, 0, 0, 0, 2, 0, -8, 0], 'aplist': [0, -1, 0, 1, -4, 6, 2, -8, -4, 6, 4, 2, -2, 12, 0, -2, -4, 6, 4, 8, -6, -16, 4, -18, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 4200, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '4200.e', 'trace_hash': 889561673478012361}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.053610792310452755323061195361', 'prec': 107}, 'conductor': 4200, 'gens': [], 'heights': [], 'lmfdb_label': '4200.e4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.36840590733117688762306228471', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4736236293247075504922491388506469591', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-43, 0, 1]], 'xcoord_integral_points': [-43]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': 'a', '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '4200.e4'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 219180
    {'degree': 2, 'field': [-35, 0, 1], 'lmfdb_label': '4200.e4', 'torsion': [4]}
  • id: 219181
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '4200.e4', 'torsion': [4]}
  • id: 219179
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '4200.e4', 'torsion': [2, 2]}
  • id: 219182
    {'degree': 4, 'field': [81, 0, -17, 0, 1], 'lmfdb_label': '4200.e4', 'torsion': [2, 4]}
  • id: 219183
    {'degree': 4, 'field': [1260, 0, -70, 0, 1], 'lmfdb_label': '4200.e4', 'torsion': [2, 4]}
  • id: 219186
    {'degree': 8, 'field': [121, -88, 32, -60, 26, 0, 8, -4, 1], 'lmfdb_label': '4200.e4', 'torsion': [8]}
  • id: 219187
    {'degree': 8, 'field': [189, -918, 720, -486, 180, -24, -12, 0, 1], 'lmfdb_label': '4200.e4', 'torsion': [6]}
  • id: 219185
    {'degree': 8, 'field': [2401, 0, 0, 0, -238, 0, 0, 0, 1], 'lmfdb_label': '4200.e4', 'torsion': [8]}
  • id: 219184
    {'degree': 8, 'field': [99225, 0, 0, 0, 595, 0, 0, 0, 1], 'lmfdb_label': '4200.e4', 'torsion': [4, 4]}
  • id: 219192
    {'degree': 16, 'field': [-12581775, -33394050, -32082750, -7736250, 7769700, 4317150, -1293050, -919990, 179510, 94930, -20810, -5070, 1684, 146, -70, -2, 1], 'lmfdb_label': '4200.e4', 'torsion': [12]}
  • id: 219189
    {'degree': 16, 'field': [2601, -4896, 4608, -3612, 14686, -22116, 18120, -8236, 239, 2108, -1240, 332, 66, -84, 32, -8, 1], 'lmfdb_label': '4200.e4', 'torsion': [2, 8]}
  • id: 219191
    {'degree': 16, 'field': [4060, -35840, 184380, -459760, 747740, -819840, 640684, -345608, 123966, -21068, -3764, 3606, -976, 92, 24, -8, 1], 'lmfdb_label': '4200.e4', 'torsion': [2, 6]}
  • id: 219188
    {'degree': 16, 'field': [257161, 926124, -65306, -1663956, 703164, 107996, 52598, -99348, 57541, -27420, 11578, -3948, 1204, -280, 60, -8, 1], 'lmfdb_label': '4200.e4', 'torsion': [2, 8]}
  • id: 219193
    {'degree': 16, 'field': [455625, 0, 0, 0, 99400, 0, 0, 0, 6750, 0, 0, 0, 180, 0, 0, 0, 1], 'lmfdb_label': '4200.e4', 'torsion': [12]}
  • id: 219190
    {'degree': 16, 'field': [424401201, 0, 113084748, 0, 48323898, 0, -1721664, 0, 414435, 0, 9856, 0, -182, 0, 28, 0, 1], 'lmfdb_label': '4200.e4', 'torsion': [2, 8]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 79040
    {'conductor': 4200, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '4200.e4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 79041
    {'conductor': 4200, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '4200.e4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 79042
    {'conductor': 4200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '4200.e4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 79043
    {'conductor': 4200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4200.e4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1691323
    {'adelic_gens': [[323, 316, 362, 741], [1, 0, 8, 1], [833, 8, 832, 9], [1, 8, 0, 1], [1, 4, 4, 17], [248, 3, 365, 2], [332, 839, 649, 834], [281, 8, 284, 33], [7, 6, 834, 835], [739, 738, 538, 115]], 'adelic_image': '840.48.0.?', 'conductor': 4200, 'lmfdb_label': '4200.e4', 'prime': 0}
  • id: 20898
    {'conductor': 4200, 'elladic_image': '4.12.0.8', 'lmfdb_label': '4200.e4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 4200.e does not appear in ec_padic